CA Foundation · Quantitative Aptitude · Theoretical Distributions
A random variable X follows a binomial distribution with n = 20 and p = 0.3. What is the variance of X?
The variance of a binomial distribution is npq. With n = 20, p = 0.3 and q = 0.7, the variance is 20 × 0.3 × 0.7 = 4.2. The figure 6 is only the mean np, not the variance.
- A6
- B4.2Correct
- C14
- D1.8
Explanation
Variance = npq = 20 × 0.3 × 0.7 = 4.2. The value 6 is the mean np, so it is wrong because it is not the variance. The value 14 is nq, which uses the wrong formula.
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